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Algebra Level 4

Find the largest possible product \(n\cdot m\) of two distinct positive integers \(n\) and \(m,\) such that the equations \( (x+1)^n=x^n+1\) and \((x+1)^m=x^m+1\) have the same set of complex roots.

Details and assumptions

The multiplicities of the roots can, of course, be different, but each root of one equation is a root of the other.

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